Fluid film bearings often operate under starved conditions. That is, the oil flowrate that is available at the inlet to the loaded pad(s) is only a fraction of the flow required by the “flooded” pad condition. The inadequate flowrate can be a result of restrictions in the supply like or in the axial groove, or due to undersized or malfunctioning oil pumps. In addition, bearings, that are operated by oil rings, or wick or splash lubrication, usually operate in starved conditions.

Numerous analyses in the past have considered free boundary lubrication problems, from the early work of Jakobsson and Floberg [8], Birkhoff and Hays [9], Cryer [10], Etsion and Pinkus [2] [3], to the more recent works of Bonneau and Frene [12] and Bayada [11], to name a few. Most of these treatments, however, are isoviscous or do not consider the coupling of the Reynolds and energy equations. In most instances the analysis is only applicable to a very short or infinitely long bearings.

The present analysis introduces a transformation of the temperature variable that allows direct solution of the energy equation for the most significant terms. The second order terms are then accounted for by direct iteration. This technique avoids the divergence that would otherwise result in the iterations for solving the coupled Reynolds and energy equations. The inclusion of the δT/δν and δθ1/ δν terms (where ν = ex, ey, or their time derivatives) during the calculation o the stiffness and damping coefficients is important, particularly at highly starved conditions.